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若干马尔可夫过程的极小充分统计量与极大似然估计量的显式极限结果：指数族方法AI 解读

Finite-state Markov chains with either a discrete or continuous time parameter, Markov renewal processes and Markov-additive processes are considered. We prove that their likelihood functions, in the nonsequential as well as in various sequential cases, belong to special $(n + k, n)$-curved exponential families in general, for which limit results are easily established. Subsequently, asymptotic normality of the corresponding nonsequential and sequential maximum likelihood…

指数型随机过程中的有效序贯估计AI 解读

A class of random processes whose likelihood functions are of exponential type is considered. A necessary and sufficient condition for a stopping time to be efficient (in the Cramer-Rao sense) is proved. This result is obtained after proving a characterization theorem, which asserts that after a suitable random-time transformation such processes become processes with stationary independent increments, by applying the solution of the problem of efficient sequential estimation…